Multi-objective optimization design of integrated pump station based on NSGA-III Open Access

With the development of the urban economy and population, the scale of cities is constantly expanding, and the demand for urban water supply is increasing. The contradiction between supply and demand has brought new challenges to water supply enterprises. The main problems are, first, fluctuations in the pressure of the water distribution system (WDS) are sometimes significant, the water pressure at some points of WDS is insufficient during peak hours; second, high energy consumption and low efficiency of water supply equipment; third, insufficient reliability and elasticity of WDS; fourth, high leakage rate of WDS; fifth, the water age of the storage facilities can lead to the risk of poor water quality (Mala-Jetmarova et al. 2017). Optimal scheduling is an important means of WDS operation and management, which plays an important role in ensuring water supply requirements and energy conservation.

Direct pressurization in municipal water supply systems has many advantages such as energy conservation, no pollution, small area occupation, fast installation, reliable operation, and easy maintenance. However, pressurized water supply equipment is not suitable for highly concentrated consumers or areas requiring high supply reliabilities (Fengguo et al. 2017). In recent years, some cities have overused pressurized water supply equipment for local pressurization, resulting in excessive water pumping from municipal main pipes, which leads to low pressure in the pipe network during peak hours, and water supply in some areas is not guaranteed. These problems have become one of the typical problems faced by WDS in the process of urbanization. Tanks play an important role in the operation and managing the supply and demand of the network (Abunada et al. 2014). The pump station equipped with a traditional ground water storage tank (GWST) can contribute to regulating water supply quantity which improves the resilience of the water supply system; however, this method cannot effectively utilize the pressure of inlet water, resulting in higher energy consumption. Hence, a new type of pump station called an integrated pump station (IPS) is adopted in the case study, which combines the booster pump (BP) with the water storage tank pump (WSTP). The BP extracts water from the municipal pipeline network, whereas the WSTP retrieves water from a storage tank. The prominent advantage of IPS mode is that it improves the reliability and resilience of the water supply system. When the residual pressure of the WDS is sufficient, the BP can be used as the main mode of operation. During peak hours, to avoid pressure fluctuations at the front, the WSTP mode can be adopted. This research mainly discusses the optimization scheduling problem for this new type of pump station.

The decision variables in a traditional optimal scheduling problem consist of the state combinations of pumps and valves. The main objective function is the total energy consumption of water supply, and other objective functions such as total energy cost (Odan et al. 2015; Fooladivanda & Taylor 2017; Cimorelli et al. 2020), water age (Prasad & Walters 2006; Al-Jasser 2007), and water quality (Mala-Jetmarova et al. 2015; Shokoohi et al. 2017) are also considered for multi-objective optimization. The constraints of optimal scheduling are numerous and complex, including pipe network hydraulic constraints (Bagirov et al. 2013), node pressure control constraints (Makaremi et al. 2017), pump operation constraints (Zhuan & Xia 2013; Quintiliani & Creaco 2019), water level constraints (Costa et al. 2016; Oikonomou et al. 2018), etc. While the direct scheduling model is relatively simple, optimizing it in a large and complex WDS poses a significant challenge. This is attributed to the substantial number of pumps and valves, further complicated by their different categorizations.

The optimal scheduling of WDS is a typical mixed integer optimization problem (Wu et al. 2012), which contains a large number of non-convex and nonlinear constraints. Additionally, it has been demonstrated to be an NP-hard problem with extremely high computational complexity (Bagloee et al. 2018; Zamzam et al. 2018). The optimization algorithms for solving the optimization scheduling problem of WDS mainly include the exact algorithm and heuristic algorithm. The exact algorithm models the optimization scheduling problem of WDS mathematically and solves the problem using conventional deterministic mathematical models based on the problem's analytical features. The main methods include dynamic programming (DP) (Lansey & Awumah 1994), linear programming (LP) (Price & Ostfeld 2014), nonlinear programming (NLP) (Bonvin et al. 2021), mixed integer nonlinear programming (MINLP) (Bragalli et al. 2012), mixed integer linear programming (MILP) (Liu et al. 2020; Salomons & Housh 2020), and hybrid solution (Vieira & Ramos 2008). In addition to the exact algorithm, another type of solving algorithm is the heuristic algorithm. Due to the large non-convex and nonlinear calculations involved in pipe network adjustments and constraints, obtaining analytical solutions with exact algorithms is challenging (Hooshmand et al. 2021). Therefore, heuristic algorithms are widely used to solve the optimization scheduling problem of WDS. The research on heuristic algorithms is very rich, with genetic algorithms (GA) (Mora-Melia et al. 2013; Perea et al. 2020) as the representative. The advantage of heuristic algorithms is that they do not require complex derivative calculations and initial values for decision variables. Compared with exact algorithms, these heuristic methods are more likely to obtain global optimal solutions. For small-scale pipe networks, using heuristic algorithms to solve optimal scheduling problems may have relatively high computational complexity. However, for larger-scale optimal scheduling problems, heuristic methods may be the only feasible solution method (Xu & Zhang 2023). Other commonly used heuristic algorithms include fast non-dominated sorting genetic algorithm (NSGA-II) (Artina et al. 2012; Makaremi et al. 2017), NSGA-III (Tao et al. 2022), particle swarm optimization (PSO) (Patel & Goyal 2016), ant colony optimization (ACO) (Afshar et al. 2015), and so on.

Compared to PSO and ACO, GA has better global search capabilities. However, NSGA-II can only handle low-dimensional optimization problems with a target dimension of ≤3, once the dimension increases, the non-dominated individuals in the population increase exponentially, making it difficult to distinguish between good and bad individuals based on Pareto dominance. NSGA-III is developed based on NSGA-II and uses the reference point method to select individuals (Deb & Jain 2013). NSGA-III is superior to NSGA-II in terms of algorithm robustness, solution quality, population diversity, and constraint scalability. Therefore, this research adopts the NSGA-III algorithm.

Overall, scholars have studied the optimal scheduling problem of WDS from different perspectives, some scholars such as Kurek & Ostfeld (2013) have conducted a comprehensive analysis, but it is only based on theoretical models. At present, there are limited real case studies available on the joint scheduling of water tank filling and pump frequency conversion. This research takes the WDS of S city in China as an example and utilizes NSGA-III to optimize the operation of the IPS. The results show that the IPS can play a role in energy conservation, water age optimization, and ‘peak shaving’ while ensuring regional water supply demand.

In this research, two types of indicators are designed: energy consumption and water age. The optimal scheduling model is constructed from the perspectives of hydraulics and water quality.

The decision variables are the pump speed ratio and the water tank inflow. The fitness of different individuals in the GA population is evaluated based on the total energy consumption of regional pump stations, and the average water age of each IPS. Additionally, penalty function constraints are added separately to eliminate unsuitable solutions.

• (1) water level range

  

  (6)

  where is the minimum limit of water level, m; is the maximum limit of water level, m; is the number of water tanks in all IPSs.

As the outlet pipe of the water tank is positioned higher than the tank's bottom, complete drainage of the water in the tank is not possible. Therefore, in the following cases, the minimum limit of the water level is taken as 0.2 m, the maximum limit of the water level is taken as 10.2 m, and the maximum effective water depth is 10 m.

• (2) 24-h cycle water level (penalty function)

There are two types of pumps for IPS, BP and WSTP, both of which are variable frequency pumps. The BP uses municipal water for direct boosting, which can utilize higher residual pressure; while the WSTP boosts the water from the storage tank, which can utilize lower residual pressure. Therefore, the BP is more energy-efficient.

The railway station (RS) and the municipal party committee (MPC) are two areas with high water demand, as shown in Figure 2. Among them, the daily water demand of the RS area is 14,333 m³ (about 5.7% of the total daily water supply), and the daily water demand of the MPC area is 7,667 m³ (about 3.1% of the total daily water supply). Due to the incomplete construction of urban pipe networks and pump stations, water pressure often falls short during peak hours (8:00–10:00, 21:00–23:00) in the two specific areas. As a result, the water supply company frequently receives complaints from residents experiencing water outages. Furthermore, the ground elevation fluctuation within the two regions is relatively large, and some users at high altitudes and high building floors have always suffered from water shortages.

Improving the problem of insufficient pressure in local areas can generally be achieved in two ways. First, using a unified pressurized water supply model (i.e. By increasing the pressure of water from water plants) to solve the problem, but this approach can lead to excess pressure in most of the pipe network, high energy consumption, and high leakage loss. Second, adding local regulation and pressurization facilities, such as GWST pump station, BP station, and the IPS recommended in the case study. Comparatively speaking, the construction of an IPS to solve the problem of insufficient regional pressure and water supply security is theoretically a better choice and is also the focus of this research.

The hydraulic model constructed in this project covers all pipelines with a diameter of 100 mm or greater. The model data were selected on 7 June 2021, and the hydraulic model simulation time step was 1 h, with a total duration of 24 time periods. After establishing the model, a verification assessment of model accuracy was conducted, and the model simulation results were consistent with the actual situation of the WDS. All pressure errors were within 1.0 m, and flow errors were within 10%. Therefore, the model meets the analysis requirements.

Using this model to analyze the current situation, the RS and MPC areas do experience insufficient pressure during peak hours. The minimum pressure of critical node in the RS area is around 8 m (an 8-story building actually requires a water head of 36 m), while the minimum pressure of critical node in the MPC area is around 12 m (a 9-story building actually requires a water head of 40 m). Therefore, water supply cannot be guaranteed.

According to the site survey, a reasonable location for the pump station was selected, and the local pipeline network was modified to separate the transmission and distribution pipelines in the RS and MPC areas. Due to the limited available space and the unsuitability for excavation in the two areas, it is difficult to use conventional GWST. In this case, the IPS with a cylindrical water tank with a height of 11 m is adopted. The main functions are as follows:

• (1) Adopting a dual mode water supply system of ‘BP + WSTP’, the BP fully utilizes the residual water pressure at the inlet of the pump, and the WSTP can also utilize the pressure of higher water level in the cylindrical water tank, achieving significant energy-saving effects.

• (2) By adopting intelligent water inlet and outlet control in the water tank, the optimal water age of the IPS can be achieved, which is conducive to ensuring downstream water quality and hygiene.

• (3) The water storage tank of the pump station can have a peak-shaving and valley-filling effect, which improves the ability to guarantee downstream water supply during peak periods, and significantly reduces the pressure fluctuation of the upstream pipeline network. Therefore, it is beneficial for the balanced operation of water plant pump stations.

The pump station's flow is designed based on the regional water demand, while the head of the pump station is designed according to the head demand at the critical node. The volume of the water tank is determined based on the water demand during the corresponding peak demand periods for a duration of 2 h. The selection of parameters for the IPS at the RS and MPC are shown in Table 1.

The operation mode of the pumps in the IPS includes three types: a. the BP works alone; b. the WSTP works alone; c. the BP and the WSTP work together. In order to minimize the energy consumption during operation and reduce the water age of the IPS, this scheme adopts plan c during peak hours and plan a during non-peak hours. There are two water tank filling modes: d. water filling throughout the whole period; e. water filling only during part of the period. In order to reduce the control complexity of the FCV, plan e is adopted for water tank filling. Water is stored during non-peak hours and supplied during peak hours, with two refilling and discharging cycles per day.

In this case study, the design of the IPS operation mode is outlined in Table 2.

Table 2

View Large

Using the NSGA-III algorithm to optimize the operating frequency of the pump (BP and WSTP) and the inlet flow rate of the water tank, while ensuring pressure at critical node meets both maximum and minimum limit requirements, the goal of simultaneously optimizing the operating energy consumption and the water age of each IPS is achieved. With a simulation time step of 1 h, an optimized operating plan is generated for the operating frequency of the pump and the inlet flow rate of the water tank within a day.

For the optimization model mentioned above, the relevant parameters are as follows:

• Population: 100

• Iteration times: 500

• Probability of mutation: 0.01

• The parameter F in differential evolution: 0.4

• Recombination probability: 0.8

• Normalized weight: w₀ = 0.001, w₁ = 0.1, w₂ = 0.1

F1 consists of two parts, where the actual energy consumption value is 1,848 and the penalty function value is 73. The penalty function value is caused by the pressure of the critical node slightly exceeding the minimum/maximum limit of set pressure.

Although the booster mode has the lowest ⁠, the of the booster mode even slightly exceeds that of the IPS mode. In addition, in the IPS mode, compared with conventional GWST, the head of the pump can be significantly reduced due to the higher available head of the cylindrical water tank. Based on experience, it is estimated that using a high cylindrical water tank can save about 10–20% energy compared to using a GWST. Overall, the comprehensive energy consumption of IPS mode is optimal.

The results show that the average water age of the MWAN in the two areas is 7.87/7.79 h, respectively, and the maximum water age is 14.08/13.52 h, respectively, both of which meet the requirements of water age that should be less than 48 h according to the regulations of the local water supply management department.

Through the construction of two regional IPSs, model simulation analysis shows that the pressure at the critical node of the RS/MPC reaches 36/40 m, respectively, meeting the water supply pressure requirements for the critical node in each area. By setting the pressure penalty function for the critical node, it is guaranteed that the pressure will not be overly redundant. In practical engineering, the pressure at the critical node can be maintained within a reasonable range through the application of end-constant pressure control technology.

This research proposes an IPS solution to solve the problem of insufficient pressure during peak hours in two local areas. The NSGA-Ⅲ multi-objective optimization algorithm is used to optimize the decision variables, and the optimal solution is verified by a hydraulic simulation using EPANET. The results demonstrate that energy conservation and water age optimization can be accomplished while ensuring a safe water supply, effectively reducing the fluctuation intensity of the total water supply from the water plants. The relevant conclusions of this design case are as follows:

• 1. The unified pressurized water supply mode has high energy consumption and is not economical, which can cause pressure redundancy in most WDS and increase the amount of water leakage. The mode of local pressurization is more economical and reasonable, which can make the spatiotemporal pressure of WDS more balanced. Among various modes of local pressurization, the IPS mode is optimal, which strikes a good balance between safe water supply and low energy costs.

• 2. By optimizing the operation mode of the water tank in the IPS, the average water age of the MWAN in the two areas is 7.87/7.79 h, respectively, and the maximum water age is 14.08/13.52 h, respectively, both of which meet the requirements of water quality.

• 3. The construction of IPSs can enhance the resilience of the WDS and reduce the fluctuation intensity of the total water supply from the water plants, which is 2,203 and 1,904 m³ /h, respectively, before and after the construction of IPSs. It can be seen that the water plant's total supply is more balanced after the construction of IPSs.

• 4. The IPS designed in this case has the advantages of small footprint, good energy saving, adjustable storage, and controllable water age. Under the policy guidance of ‘energy conservation and dual carbon’ and ‘urban resilience’, it is likely to gain more market favor in the future, especially in densely populated cities with undulating terrain. NSGA-Ⅲ algorithm has the advantages of robustness, population diversity, and constraint scalability, and has good results for such multi-objective optimization problems.

We thank the water company for providing the basic information. We also thank the anonymous reviewers and editors for their comments and suggestions.

R. L. collected the data, rendered support in modeling and programming design, developed the methodology, visualized the data, and wrote the initial draft; H. W. rendered support in programming design and visualization; K. X. rendered support in funding acquisition, supervised the work, and wrote revisions; T. T. wrote revisions.

This work was financially supported by National Natural Science Foundation of China [grant numbers: 52270093].

All authors give their consent to participate.

All authors give their consent to publish.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.